Hidalgo, I have hunted antelope in many different ways and with many different weapons. Although it would seem that some of these guys are telling you that you could never get close to a "Trophy antelope".
I can tell you from first hand experience that all you have to do is do your home work as with anything else.
I have used a Bow and the best one with a bow was 18", I have also shot one with a Rem. XP-100 pistol chambered in .223 and was a 230 yard shot that lope was 17 3/8". So as you can see these are all on the low end of things, these animals are very thin skinned and are some what fragile.
So the answer to your question I would say that a .243AI would be my choice!
Good luck
Kapac